Finite Group DatabasebetaFinite Group Databasebeta| order | 10948 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D17×D161 |
| unambiguous semidirect product | (C7×D17)⋊D23 |
| unambiguous semidirect product | (C23×D17)⋊D7 |
| Fitting, socle, derived, Hall | C7×C17×C23 ⋊ C22 |
| Hall | C17×C23 ⋊ C2×D7 |
| Hall | C7×C23 ⋊ C2×D17 |
| Hall | C7×C17 ⋊ C2×D23 |
| Sylow | C23 ⋊ D7×D17 |
| Sylow | C17 ⋊ C2×D161 |
| Sylow | C7 ⋊ D17×D23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C17×C23 | C22 |
| LCS | G ▷ C7×C17×C23 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
820 conjugacy classes — view the full character table.
| maximal subgroup of | D17×ΓL(1,𝔽8)⋊D23, C3×D17×D161, D17×D483, … |
| maximal normal subgroup of | D17×ΓL(1,𝔽8)⋊D23, C3×D17×D161 |
| maximal quotient of | C3×D17×D161, D17×D483, D51×D161, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10948, 18);